Solve for c -15=-2c^2-7

$- 15 = - 2 c^{2} - 7$

Rewrite the equation as $- 2 c^{2} - 7 = - 15$ .

$- 2 c^{2} - 7 = - 15$

Move all terms not containing $c$ to the right side of the equation.

Add $7$ to both sides of the equation.

$- 2 c^{2} = - 15 + 7$

Add $- 15$ and $7$ .

$- 2 c^{2} = - 8$

Divide each term in $- 2 c^{2} = - 8$ by $- 2$ and simplify.

Divide each term in $- 2 c^{2} = - 8$ by $- 2$ .

$\frac{- 2 c^{2}}{- 2} = \frac{- 8}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 c^{2}}{- 2} = \frac{- 8}{- 2}$

Divide $c^{2}$ by $1$ .

$c^{2} = \frac{- 8}{- 2}$

Simplify the right side.

Divide $- 8$ by $- 2$ .

$c^{2} = 4$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$c = \pm \sqrt{4}$

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

$c = \pm \sqrt{2^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$c = \pm 2$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$c = 2$

Next, use the negative value of the $\pm$ to find the second solution.

$c = - 2$

The complete solution is the result of both the positive and negative portions of the solution.

$c = 2, - 2$